Tabla de i

Apuntes

Tabla de integrales www.vaxasoftware.com/indexes.html C ∫+ = C dx ∫+ x kdx kx = C 2 ∫+ xdx x = C 2 3 2 x ∫+ x dx = C 3 n + 1 n + 1 x dx = + C ≠ ∫− u ' n x dx = + C ≠ n ∫− , ( n ) 1 u u , ( n ) 1 n + 1 n + 1 ' dx ln ∫+ = C 1 ∫+ x u ln dx = C u x u ' dx ∫+ x 1 ∫+ = ln x + a C u ln dx = u + a + a u + a dx x ∫+ e = C x C e ∫ u u u ' + e dx = e x u a dx + C ( > 0 ∫≠ a a = ) 1 u a a dx ' a + C > , 0 x ∫≠ , , u a = ) 1 , ( a ln a ln a ∫+ sen xdx cos = C − x ' udx − ∫+ sen u cos = C u ∫+ cos xdx sen = C x ' ∫+ u sen cos udx = C u 1 ' dx tan ∫+ u = C x dx tan cos 2 ∫+ = C u 2 x cos u ∫+ 1 ( 2 + C tan x tan ) dx = x ' 2 tan u tan dx = ∫+ 1 ( + C u ) u 1 ' dx − cotan ∫+ u = C x dx − cotan sen 2 ∫+ = C u 2 x sen u 1 ' dx = ∫+ u arcsen x C dx = 2 ∫+ arcsen u 1 − x 1 2 − u 1 ' dx = arctan ∫+ u x C dx = arctan 1 + x 2 ∫+ u 1 2 + u C 1 1 ' x dx = arctan ∫+ u 1 u C dx = arctan 2 ∫+ 2 a a 2 2 + x a a + u a a C C Integral de la suma o resta ( ± ∫ ∫ ∫ ± vdx v dx = udx u ) udv Integración por partes ∫ ∫− = vdu uv Regla de Barrow ) ∫ b f b ( a x ) dx = F ( x ) = F ( b ) − F ( a a Siendo: u, v funciones de x; a, k, n, C constantes.